It is natural to relate partially ordered sets (posets in short) and classes of equivalent words over partially commutative alphabets. Their common graphical representation are Hasse diagrams. We investigate this relation in detail and propose an efficient online algorithm that decompresses a concurrent word to its Hasse diagram. The lexicographically minimal representative of a trace (an equiv...

Let Q(k; l) be a poset whose Hasse diagram is a regular spider with k +1 legs having the same length l (cf. Fig. 1). We show that for any n 1 the n th cartesian power of the spider poset Q(k; l) is a Macaulay poset for any k 0 and l 1. In combination with our recent results 2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices, whos...

It is natural to try to relate partially ordered sets (posets in short) and classes of equivalent words over partially commutative alphabets. Their common graphical representation are Hasse diagrams. We will investigate this relation in detail and propose an efficient on-line algorithm that decompresses a string to Hasse diagram. Further we propose a definition of the canonical representatives ...

For a prime p ≡ 5 (mod 8) satisfying certain conditions, we show that there exist an infinitude of K3 surfaces parameterized by certain solutions to Pell’s equation X2 − pY 2 = 4 in the projective 5-space that are counterexamples to the Hasse principle explained by the Brauer-Manin obstruction. Further, these surfaces contain no zero-cycle of odd degree over Q. As an illustration for the main r...

As the causal relationships induced by communication between cooperating processes are crucial for understanding the dynamic behavior of parallel and distributed systems, tool support is needed for analyzing them. This paper presents hasse, a tool which graphically represents the event traces from cooperating processes according to a formal description of their causal interdependences. Hasse al...

In this lecture we give an introduction to the Grothendieck ring of algebraic varieties, and discuss Kapranov’s lifting of the Hasse-Weil zeta function to this Grothendieck ring. One interesting feature is that this makes sense over an arbitrary field. We will prove the rationality of Kapranov’s zeta function for curves by a variant of the argument used in Lecture 4 for the Hasse-Weil zeta func...

This preprint is intended to provide a general reference for jet spaces and jet differentials, valid in maximal generality (at the level of EGA). The approach is rather concrete, using Hasse-Schmidt (divided) higher differentials. Discussion of projectivized jet spaces (as in Green and Griffiths [G-G]) is included. This paper contains a few brief notes on how to define jets using Hasse-Schmidt ...

We study the distribution of Brauer group and frequency Brauer–Manin obstruction to Hasse principle weak approximation in a family smooth del Pezzo surfaces degree four over rationals.

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

The CoI2(PPh3)2/Zn system effectively catalyzes the [2 + 2 + 2] ene-diyne cycloaddition of 1,6-heptadiynes with allenes in a highly regio- and chemoselective fashion to yield substituted benzene derivatives in good to excellent yields.